"The double integral $\displaystyle \iint_{R}^{} \, f(x,y) dx\,dy$ can be expressed as $\displaystyle \int_{\pi}^{2\pi}$$\displaystyle \int_{1}^{2}$ $\displaystyle r^2 sin(\theta) dr\,d\Theta$ in polar coordinates. What is the region R? What is the formula for f(x,y)? What is the integral in cartesian coordinates?